# Finding the circumference of a circle

“Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.”
Do you agree with this quote? Why?
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1:30
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Slide 1: Open question
MathematicsLower Secondary (Key Stage 3)

This lesson contains 45 slides, with interactive quizzes, text slides and 2 videos.

Lesson duration is: 20 min

## Items in this lesson

“Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.”
Do you agree with this quote? Why?
timer
1:30

#### Slide 1 -Open question

Circle
The parts of a circle are the radius, diameter, circumference, arc, chord, secant, tangent, sector and segment. A round plane figure whose boundary consists of points equidistant from a fixed point.
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4:00

#### Slide 2 -Slide

What is the numerical equivalent of Pi?

Pi
3.14

#### Slide 4 -Slide

What is the circumference of a circle?
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0:30
A
A line segment going from one point of the circumference to another but does not go through the centre.
B
The distance across the circle going through the centre.
C
The distance from the centre of a circle to the outside.
D
The distance once around the circle.

#### Slide 5 -Quiz

Finding the circumference of a circle using the radius

#### Slide 6 -Slide

What is the radius of a circle?
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0:30
A
A line segment going from one point of the circumference to another but does not go through the centre.
B
The distance across the circle going through the centre.
C
The distance from the centre of a circle to the outside.
D
The distance once around the circle.

#### Slide 7 -Quiz

Use the formula C = 2πr to find the circumference using the radius. In this formula, "r" represents the radius of the circle. Again, you can plug π into your calculator to get its numeral value, which is a closer approximation of 3.14.

A radius is any line segment that extends from the center of the circle and has its other endpoint on the edge of the circle.
You might notice this is similar to the C = πd formula. That’s because the radius is half as long as the diameter, so the diameter can be thought of as 2r.

Example

#### Slide 10 -Video

What is the circumference of a circle that has a radius of 6cm?
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37.7cm

#### Slide 12 -Slide

Finding the circumference of a circle using the diameter

#### Slide 13 -Slide

What is the diameter of a circle?
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0:30
A
A line segment going from one point of the circumference to another but does not go through the centre.
B
The distance across the circle going through the centre.
C
The distance from the centre of a circle to the outside.
D
The distance once around the circle.

#### Slide 14 -Quiz

Using the diameter
Use the formula C = πd to find the circumference if you know the diameter. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter.

That is to say, you can find the circumference of a circle just by multiplying the diameter by pi. Plugging π into your calculator will give you its numerical value, which is a closer approximation of 3.14 or 22/7.

Diameter means a straight line segment that passes through the center of the circle and has its endpoints on the sides of the circle.

Example

#### Slide 16 -Slide

What is the circumference of a circle that has a diameter of 9cm?
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28.8cm

#### Slide 18 -Slide

Are people born with a specific personality, or is the character the result of their circumstances?

#### Slide 20 -Slide

Finding the area of a circle using the radius (and diameter)

#### Slide 21 -Slide

What is the area of a circle?
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A
A line segment going from one point of the circumference to another but does not go through the centre.
B
The space inside a 2D shape.
C
The distance from the centre of a circle to the outside.
D
The distance once around the circle.

#### Slide 22 -Quiz

Finding the area
Square the radius. The formula to find the area of a circle is 2
A=pi r2, where the r variable represents the radius. This variable is squared.
Do not get confused and square the entire equation.

For the sample circle with radius,  r = 6 then r2 (squared) = 36

#### Slide 23 -Slide

Using the diameter...
What do you think we do?

#### Slide 25 -Video

What is the area of a circle with a radius of 4cm?

#### Slide 26 -Open question

50.27cm (squared)

What is success?

#### Slide 29 -Open question

Finding the radius of a circle using the circumference.

#### Slide 30 -Slide

What is the radius of a circle?
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0:30
A
A line segment going from one point of the circumference to another but does not go through the centre.
B
The distance across the circle going through the centre.
C
The distance from the centre of a circle to the outside.
D
The distance once around the circle.

#### Slide 31 -Quiz

Using the circumference
Write down the circumference formula. The formula is C=2\pi r, where C equals the circle’s circumference, and r equals its radii

The symbol pi ("pi") is a special number, roughly equal to 3.14. You can either use that estimate (3.14) in calculations, or use the
pi symbol on a calculator.

#### Slide 33 -Slide

What is the radius of a circle with a circumference of 20m
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3.2m

#### Slide 35 -Slide

Finding the circumference of a circle using the area.

#### Slide 36 -Slide

What is the area of a circle?
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0:30
A
The space inside a 2D shape.
B
The distance across the circle going through the centre.
C
The distance from the centre of a circle to the outside.
D
The distance once around the circle.

#### Slide 40 -Slide

Find the circumference of a circle with an area of 22cm
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16.6cm

#### Slide 42 -Slide

Practice Problems to Calculate Radius of a Circle

1. Circumference of 36π, find circle's radius.

2. Diameter is 12, what is the radius?

3. Circle's area of 113 sq units, find radius.

4. Circle's circumference of 75.4, find radius.

5. Circle's diameter of 20, determine radius.
6. Circumference of 24π, find circle's radius.

7. Circle's area of 153.94 sq units, find radius.

8. Diameter of 14, determine circle's radius.

9. Circle's circumference of 47.12, find radius.

10. Circle's area of 132 sq units, find radius.
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12:00